7.1. Conclusion
Even though the study of the complete system for DVB-S2, DVB-T2 and IEEE 802.16e standards is beyond the scope of this thesis, a detailed study and analysis of the important parts of the systems such as LDPC coding part, BCH coding, OFDM as well as polynomials for generating the short/normal FEC frame. The performance analysis provided in Chapter 6 agrees with the present publications and literature.
BER and PSNR performances of the three systems were obtained over AWGN and fading channel models (ITU- Vehicular A and ITU- Vehicular B). For AWGN channel, the best BER performance was obtained using the rate R = 1/2 LDPC code specified in IEEE 802.16e, where zero- error decoding becomes possible after an SNR of 1.5 dB. The second best BER is attained while using the rate R = 1/4 LDPC for the DVB-T2. Here zero- error decoding was shown to be possible after 3.5 dB. It has been shown that there is a coding gain of about 9 dB for a target BER of 10−2 when the IEEE 802.16e LDPC is used instead of the IEEE 802.16e RS(255;239;8) CC(2;1;7) concatenated coding. Clearly the usage of LDPC encoders brings a big improvement to the system’s BER performance. Also it has been shown that in the case of many bit errors introduced by the channel the error floor has been removed by the concatenation of an outer BCH encoder. Similar many error correcting codes LDPC codes also have a limit for the number of errors they can fix. If the errors introduced by the channel are more than this limit an error floor would be observed. It was shown by simulation that
this error floor. However the maximum number of errors the BCH-LDPC concatenated coder can fix is also limited. This is because the generator polynomials are designed to fix only a maximum number of errors. In the case of DVB-T2 this number is 12. Hence if more than 12 errors per block occurs the error floor will not be removed even using BCH-LDPC encoding.
According to the results presented in Chapter 6, when BCH-LDPC coding is used in the presence of bit errors, it is possible to receive the transmitted image without any errors after an SNR value of 3.5 dB in case of AWGN channel; but when LDPC-only is used under the same conditions, a degradation in the performance is observed. This error floor might keep the PSNR of the received image at a fairly constant value, thus limiting the received image quality. Comparing the performance results for ITU- Vehicular A and ITU-Vehicular B channels, we can see that Vehicular B channel is a more difficult channel than ITU-Vehicular A. For instance a target BER level of (10−3) can be attained at 5.5 dB and 7.5 dB respectively.
7.2. Future work
Facing the need for transmitting reliable data over the modern communications channel, many researchers focused in channel coding and in the features of LDPC codes. It is important to mention that great progress has been made in this area. As it is stated in this work LDPC codes performs best for long codeword length. However, need of the communication industry to shorten the length of codeword gives to the researchers another assignment. Shortening the LDPC codeword raise up the problem of so called “girth4”. Girth 4 cycles leads performance degradation and should be avoided.
As a future work designing the Low-Density Parity-Check matrix for shorter codeword lengths in order to extend the applications of LDPC channel coding is recommended. Some results on this issue has been published but a lot more remains to be done because even though the
LDPC codes designed give good performance they still do not attain the Shannon limit as explained in [5].
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APPENDIX
Appendix A: Addresses of parity bit accumulators
Addresses of parity bit accumulators for rate R = 2/5, nld pc= 64800 bits
c1(t) =
31413 18834 28884 947 23050 14484 14809 4968 455 33659 16666 19008 13172 19939 13354 13719 6132 20086 34040 13442 27958 16813 29619 16553 1499 32075 14962 11578 112049 9217 10485 23062 30936 17892 24204 24885 32490 18086 18007 4957 7285 32073 19038 7152 12486 13483 24808 21759 32321 10839 15620 33521 23030 10646 26236 19744 21713 36784 8016 12869 35597 11129 17948 26160 14729 31943 20416 10000 7882 31380 27858 33356 14125 12131 36199 4058 35992 36594 33698 15475 1566 18498 12725 7067 17406 8372 35437 2888 1184 30068 25802 11056 5507 26313 32205 37232 15254 5365 17308 22519 35009 718 5240 16778 23131 24092 20587 33385 27455 17602 4590 21767 22266 27357 30400 8732 5596 3060 33703 3596 6882 873 10997 24738 20770 10067 13379 27409 25463 2673 6998 31378 15181 13645 34501 3393 3840 35227 15562 23615 38342 12139 19471 15483 13350 6707 23709 37204 25778 21082 7511 14588 10010 21854 28375 33591 12514 4695 37190 21379 18723 5802 7182 2529 29936 35860 28338 10835 34283 25610 33026 31017 21259 2165 21807 37578 1175 16710 21939 30841 27292 33730 6836 26476 27539 35784 18245 16394 17939 23094 19216 17432 11655 6183 38708 28408 35157 17089 13998 36029 15052 16617 5638 36464 15693 28923 26245 9432 11675 25720 26405 5838 31851 26898 8090 37037 24418 27583 7959 35562 37771 17784 11382 11156 37855 7073 21685 34515 10977 13633 30969 7516 11943 18199 5231 13825 19589 23661 11150 35602 19124 30774 6670 37344 16510 26317 23518 22957 6348 34069 8845 20175 34985 14441 25668 4116 3019 21049 37308 24551 24727 20104 24850 12114 38187 28527 13108 13985 1425 21477 30807 8613 26241 33368 35913 32477 5903 34390 24641 26556 23007 27305 38247 2621 9122 32806 21554 18685
c2(t) =
17287 27292 19033 25796 31795 12152 12184 35088 31226 38263 33386 24892 23114 37995 29796 34336 10551 36245 35407 175 7203 14654 38201 22605 28404 6595 1018 19932 3524 29305 31749 20247 8128 18026 36357 26735
7543 29767 13588 13333 25965 8463 14504 36796 19710
4528 25299 7318 35091 25550 14798
7824 215 1248 30848 5362 17291 28932 30249 27073 13062 2103 16206 7129 32062 19612 9512 21936 38833 35849 33754 23450 18705 28656 18111 22749 27456 32187
... ... ...
28229 31684 30160 15293 8483 28002 14880 13334 12584 28646 2558 19687 6259 4499 26336 11952 28386 8405 10609 961 7582 10423 13191 26818 15922 36654 21450 10492 1532 1205 30551 36482 22153
5156 11330 34243 28616 35369 13322 8962 1485 21186 23541 17445 35561 33133 11593 19895 33917 7863 33651 20063 28331 10702 13195 21107 21859 4364 31137 4804 5585 2037 4830 30672 16927 14800
Addresses of parity bit accumulators for rate R = 3/5, nld pc= 64800 bits
c1(t) =
22422 10282 11626 19997 11161 2922 3122 99 5625 17064 8270 179 25087 16218 17015 828 20041 25656 4186 11629 22599 17305 22515 6463 11049 22853 25706 14388 5500 19245 8732 2177 13555 11346 17265 3069 16581 22225 12563 19717 23577 11555 25496 6853 25403 5218 15925 21766 16529 14487 7643 10715 17442 11119 5679 14155 24213 21000 1116 15620 5340 8636 16693 1434 5635 6516 9482 20189 1066 15013 25361 14243 18506 22236 20912 8952 5421 15691 6126 21595 500 6904 13059 6802
8433 4694 5524 14216 3685 19721 25420 9937 23813 9047 25651 16826 21500 24814 6344 17382 7064 13929 4004 16552 12818 8720 5286 2206 22517 2429 19065 2921 21611 1873 7507 5661 23006 23128 20543 19777
1770 4636 20900 14931 9247 12340 11008 12966 4471 2731 16445 791 6635 14556 18865 22421 22124 12697 9803 25485 7744 18254 11313 9004 19982 23963 18912 7206 12500 4382 20067 6177 21007 1195 23547 24837
756 11158 14646 20534 3647 17728 11676 11843 12937 4402 8261 22944 9306 24009 10012 11081 3746 24325 8060 19826 842 8836 2898 5019 7575 7455 25244 4736 14400 22981 5543 8006 24203 13053 1120 5128 3482 9270 13059 15825 7453 23747 3656 24585 16542 17507 22462 14670 15627 15290 4198 22748 5842 13395 23918 16985 14929 3726 25350 24157 24896 16365 16423 13461 16615 8107 24741 3604 25904 8716 9604 20365 3729 17245 18448 9862 20831 25326 20517 24618 13282 5099 14183 8804 16455 17646 15376 18194 25528 1777 6066 21855 14372 12517 4488 17490
1400 8135 23375 20879 8476 4084 12936 25536 22309 16582 6402 24360 25119 23586 128 4761 10443 22536 8607 9752 25446 15053 1856 4040
377 21160 13474 5451 17170 5938 10256 11972 24210 17833 22047 16108 13075 9648 24546 13150 23867 7309 19798 2988 16858 4825 23950 5125 20526 3553 11525 23366 2452 17626 19265 20172 18060 24593 13255 1552 18839 21132 20119 15214 14705 7096 10174 5663 18651 19700 12524 14033
4127 2971 17499 16287 22368 21463 7943 18880 5567 8047 23363 6797 10651 24471 14325 4081 7258 4949 7044 1078 797 22910 20474 4318 21374 13231 22985 5056 3821 23718 14178 9978 19030 23594 8895 25358
6199 22056 7749 13310 3999 23697 16445 22636 5225 22437 24153 9442 7978 12177 2893 20778 3175 8645 11863 24623 10311 25767 17057 3691 20473 11294 9914 22815 2574 8439 3699 5431 24840 21908 16088 18244
8208 5755 19059 8541 24924 6454 11234 10492 16406 10831 11436 9649 16264 11275 24953 2347 12667 19190 7257 7174 24819 2938 2522 11749
3627 5969 13862 1538 23176 6353 2855 17720 2472 7428 573 15036
c2(t) =
0 18539 18661 1 10502 3002 2 9368 10761 3 12299 7828 4 15048 13362 5 18444 24640 6 20775 19175 7 18970 10971 8 5329 19982 9 11296 18655 10 15046 20659 11 7300 22140 12 22029 14477 13 11129 742 14 13254 13813 15 19234 13273 16 6079 21122 17 22782 5828 18 19775 4247 19 1660 19413 20 4403 3649 21 13371 25851 22 22770 21784 23 10757 14131 24 16071 21617 25 6393 3725 26 597 19968 27 5743 8084 28 6770 9548 29 4285 17542 30 13568 22599 31 1786 4617 32 23238 11648 33 19627 2030 34 13601 13458 35 13740 17328 36 25012 13944 37 22513 6687
... ... ...
38 4934 125872 39 21197 5133 40 22705 6938 41 7534 24633 42 24400 12797 43 21911 25712 44 12039 1140 45 24306 1021 46 14012 20747 47 11265 15219 48 4670 15531 49 9417 14359 50 2415 6504 51 24964 24690 52 14443 8816 53 6926 1291 54 6209 20806 55 13915 4079 56 24410 13196 57 13505 6117 58 9869 8220 59 1570 6044 60 25780 17387 61 20671 24913 62 24558 20591 63 12402 3702 64 8314 1357 65 20071 14616 66 17014 3688 67 19837 946 68 15195 12136 69 7758 22808 70 3564 2925 71 3434 7769
Addresses of parity bit accumulators for rate R = 2/3, nld pc= 64800 bits
c1(t) =
0 10491 16043 506 12826 8065 8226 2767 240 18673 9279 10579 20928 1 17819 8313 6433 6224 5120 5824 12812 17187 9940 13447 13825 18483 2 17957 6024 8681 18628 12794 5915 14576 10970 12064 20437 4455 7151 3 19777 6183 9972 14536 8182 17749 11341 5556 4379 17434 15477 18532 4 4651 19689 1608 659 16707 14335 6143 3058 14618 17894 20684 5306 5 9778 2552 12096 12369 15198 16890 4851 3109 1700 18725 1997 15882 6 486 6111 13743 11537 5591 7433 15227 14145 1483 3887 17431 12430 7 20647 14311 11734 4180 8110 5525 12141 15761 18661 18441 10569 8192 8 3791 14759 15264 19918 10132 9062 10010 12786 10675 9682 19246 5454 9 19525 9485 7777 19999 8378 9209 3163 20232 6690 16518 716 7353 10 4588 6709 20202 10905 915 4317 11073 13576 16433 368 3508 21171 11 14072 4033 19959 12608 631 19494 14160 8249 10223 21504 12395 4322
(7.5)
c2(t) =
12 13800 14161 13 2948 9647 14 14693 16027 15 20506 11082 16 1143 9020 17 13501 4014 18 1548 2190 19 12216 21556 20 2095 19897 21 4189 7958 22 15940 10048 23 515 12614 24 8501 8450 25 17595 16784 26 5913 8495 27 16394 10423 28 7409 6981 29 6678 15939 30 20344 12987 31 2510 14588 32 17918 6655 33 6703 19451 34 496 4217 35 7290 5766 36 10521 8925 37 20379 11905 38 4090 5838 39 19082 17040 40 20233 12352 41 19365 19546 42 6249 19030 43 11037 19193 44 19760 11772 45 19644 7428 46 16076 3521 47 11779 21062 48 13062 9682 49 8934 5217
... ... ...
50 11087 3319 51 18892 4356 52 7894 3898 53 5963 4360 54 7346 11726 55 5182 5609 56 2412 17295 57 9845 20494 58 6687 1864 59 20564 5216 0 18226 17206 1 9380 8266 2 7073 3065 3 18252 13437 4 9161 15642 5 10714 10153 6 11585 9078 7 5359 9418 8 9024 9515 9 1206 16354 10 14994 1102 11 9375 20796 12 15964 6027 13 14789 6452 14 8002 18591 15 14742 14089 16 253 3045
... ... ...
17 1274 19286 18 14777 2044 19 13920 9900 20 452 7374 21 18206 9921 22 6131 5414 23 10077 9726 24 12045 5479 25 4322 7990 26 15616 5550 27 15561 10661 28 20718 7387 29 2518 18804 30 8984 2600 31 6516 17909 32 11148 98 33 20559 3704 34 7510 1569 35 16000 11692 36 9147 10303 37 16650 191 38 15577 18685 39 17167 20917 40 4256 3391 41 20092 17219 42 9218 5056 43 18429 8472 44 12093 20753 45 16345 12748 46 16023 11095 47 5048 17595 48 18995 4817 49 16483 3536 50 1439 16148 51 3661 3039 52 19010 18121 53 8968 11793 54 13427 18003 55 5303 3083 56 531 16668 57 4771 6722 58 5695 7960 59 3589 14630
Addresses of parity bit accumulators for rate R = 3/4, nld pc= 64800 bits
c1(t) =
0 6385 7901 14611 13389 11200 3252 5243 2504 2722 821 7374 1 11359 2698 357 13824 12772 7244 6752 15310 852 2001 11417 2 7862 7977 6321 13612 12197 14449 15137 13860 1708 6399 13444 3 1560 11804 6975 13292 3646 3812 8772 7306 5795 14327 7866 4 7626 11407 14599 9689 1628 2113 10809 9283 1230 15241 4870 5 1610 5699 15876 9446 12515 1400 6303 5411 14181 13925 7358 6 4059 8836 3405 7853 7992 15336 5970 10368 10278 9675 4651 7 441 3963 9153 2109 12683 7459 12030 12221 629 15212 406 8 6007 8411 5771 3497 543 14202 875 9186 6235 13908 3563 9 3232 6625 4795 546 9781 2071 7312 3399 7250 4932 12652 10 8820 10088 11090 7069 6585 13134 10158 7183 488 7455 9238 11 1903 10818 119 215 7558 11046 10615 11545 14784 7961 15619 12 3655 8736 4917 15874 5129 2134 15944 14768 7150 2692 1469 13 9316 3820 505 8923 6757 806 7957 4216 15589 13244 2622 14 14463 4852 15733 3041 11193 12860 13673 8152 6551 15108 8758
(7.7)
c2(t) =
15 3149 11981 16 13416 6906 17 13098 13352 18 2009 14460 19 7207 4314 20 3312 3945 21 4418 6248 22 2669 139754 23 7571 9023 24 14172 2967 25 7271 7138 26 6135 13670 27 7490 6981 28 8657 2466 29 8599 12834 30 3470 3152 31 13917 4365 32 6024 13730 33 10973 14182 34 2464 13167 35 5281 15049 36 1103 1849 37 2058 1069 38 9654 6095 39 14311 7667 40 15617 8146 41 4588 11218 42 13660 6243 43 8578 7874 44 11741 2686 0 1022 1264 1 12604 9965 2 8217 2707 3 3156 11793 4 354 1514 5 6978 14058 6 7922 16079 7 15087 12138 8 5053 6470 9 12687 14932 10 15458 1763 11 8121 1721 12 12431 549
... ... ...
13 4129 7091 14 1426 8415 15 9783 7604 16 6295 11329 17 1409 12061 18 8065 9087 19 2918 8438 20 1293 14115 21 3922 13851 22 3851 4000 23 5865 1768 24 2655 14957 25 5565 6332 26 4303 12631 27 11653 12236 28 16025 7632 29 4655 14128 30 9584 13123 31 13987 9597 32 15409 12110 33 8754 15490 34 7416 15325 35 2909 15549 36 2995 8257 37 9406 4791 38 11111 4854 39 2812 8521 40 8476 14717 41 7820 15360 42 1179 7939 43 2357 8678 0 3477 7067 1 3931 13845 2 7675 12899 3 1754 8187 4 7785 1400 5 9213 5891 6 2494 7703 7 2576 7902 8 4821 15682 9 10426 11935
... ... ...
10 1810 904 11 11332 9264 12 11312 3570 13 14916 2650 14 7679 7842 15 6089 13084 16 3938 2751 17 8509 4648 18 12204 8917 19 5749 12433 20 12613 4431 21 1344 4014 22 8488 13850 23 1730 14896 24 14942 7126 25 14983 8863 26 6578 8564 27 4947 396 28 297 12805 29 13878 6692 30 11857 11186 31 14395 11493 32 16145 12251 33 13462 7428 34 14526 13119 35 2535 11243 36 6465 12690 37 6872 9334 38 15371 14023 39 8101 10187 40 11963 4848 41 15125 6119 42 8051 14465 43 11139 5167 42 2883 14521
Addresses of parity bit accumulators for rate R = 4/5, nld pc= 64800 bits
c1(t) =
0 149 11212 5575 6360 12559 8108 8505 408 10026 12828 1 5237 490 10677 4998 3869 3734 3092 3509 7703 10305 2 8742 5553 2820 7085 12116 10485 564 7795 2972 2157 3 2699 4304 8350 712 2841 3250 4731 10105 517 7516 4 12067 1351 11992 12191 11267 5161 537 6166 4246 2363 5 6828 7107 2127 3724 5743 11040 10756 4073 1011 3422 6 11259 1216 9526 1466 10816 940 3744 2815 11506 11573 7 4549 11507 1118 1274 11751 5207 7854 12803 4047 6484 8 8430 4115 9440 413 4455 2262 7915 12402 8579 7052 9 3885 9126 5665 4505 2343 253 4707 3742 4166 1556 10 1704 8936 6775 8639 8179 7954 8234 7850 8883 8713 11 11716 4344 9087 11264 2274 8832 9147 11930 6054 5455 12 7323 3970 10329 2170 8262 3854 2087 12899 9497 11700 13 4418 1467 2490 5841 817 11453 533 11217 11962 5251 14 1541 4525 7976 3457 9536 7725 3788 2982 6307 5997 15 11484 2739 4023 12107 6516 551 2572 6628 8150 9852 16 6070 1761 4627 6534 7913 3730 11866 1813 12306 8249 17 12441 5489 8748 7837 7660 2102 11341 2936 6712 11977
(7.9)
c2(t) =
18 10155 4210 19 1010 10483 20 8900 10250 21 10243 12278 22 7070 4397 23 12271 3887 24 11980 6836 25 9514 4356 26 7137 10281 27 11881 2526 28 1969 11477 29 3044 10921 30 2236 8724 31 9104 6340 32 7342 8582 33 11675 10405 34 6467 12775 35 3186 12198 0 9621 11445 1 7486 5611 2 4319 4879 3 2196 344 4 7527 6650 5 10693 2440 6 6755 2706 7 5144 5998 8 11043 8033 9 4846 4435 10 4157 9228 11 12270 6562 12 11954 7592 13 7420 2592 14 8810 9636 15 689 5430 16 920 1304 17 253 11934 18 9559 6016 19 312 7589 20 4439 4197 21 4002 9555 22 12232 7779 23 1494 8782 24 10749 3969
... ... ...
25 4368 3479 26 6316 5342 27 2455 3493 28 12157 7405 29 6598 11495 30 11805 4455 31 9625 2090 32 4731 2321 33 3578 2608 34 8504 1849 35 4027 1151 0 5647 4935 1 4219 1870 2 10968 8054 3 6970 5447 4 3217 5638 5 8972 669 6 5618 12472 7 1457 1280 8 8868 3883 9 8866 1224 10 8371 5972 11 266 4405 12 3706 3244 13 6039 5844 14 7200 3283 15 1502 11282 16 12318 2202 17 4523 965 18 9587 7011 19 2552 2051 20 12045 10306 21 11070 5104 22 6627 6906 23 9889 2121 24 829 9701 25 2201 1819 26 6689 12925 27 2139 8757 28 12004 5948 29 8704 3191
... ... ...
30 8171 10933 31 6297 7116 32 616 7146 33 5142 9761 34 10377 8138 35 7616 5811 0 7285 9863 1 7764 10867 2 12343 9019 3 4414 8331 4 3464 642 5 6960 2039 6 786 3021 7 710 2086 8 7423 5601 9 8120 4885 10 12385 11990 11 9739 10034 12 424 10162 13 1347 7597 14 1450 112 15 7965 8478 16 8945 7397 17 6590 8316 18 6838 9011 19 6174 9410 20 255 113 21 6197 5835 22 12902 3844 23 4377 3505 24 5478 8672 25 44531 2132 26 9724 1380 27 12131 11526 28 12323 9511 29 8231 1752 30 497 9022 31 9288 3080 32 2481 7515 33 2696 268 34 4023 12341 35 7108 5553
Addresses of parity bit accumulators for rate R = 5/6, nld pc= 64800 bits
c1(t) =
0 4362 416 8909 4156 3216 3112 2560 2912 6405 8593 4969 6723 1 2479 1786 8978 3011 4339 9313 6397 2957 7288 5484 6031 10217 2 10175 9009 9889 3091 4985 7267 4092 8874 5671 2777 2189 8716 3 9052 4795 3924 3370 10058 1128 9996 10165 9360 4297 434 5138 4 2379 7834 4835 2327 9843 804 329 8353 7167 3070 1528 7311 5 3435 7871 348 3693 1876 6585 10340 7144 5870 2084 4052 2782 6 3917 3111 3476 1304 10331 5939 5199 1611 1991 699 8316 9960 7 6883 3237 1717 10752 7891 9764 4745 3888 10009 4176 4614 1567 8 10587 2195 1689 2968 5420 2580 2883 6496 111 6023 1024 4449 9 3786 8593 2074 3321 5057 1450 3840 5444 6572 3094 9892 1512 10 8548 1848 10372 4585 7313 6536 6379 1766 9462 2456 5606 9975 11 8204 10593 7935 3636 3882 394 5968 8561 2395 7289 9267 9978 12 7795 74 1633 9542 6867 7352 6417 7568 10623 725 2531 9115 13 7151 2482 4260 5003 10105 7419 9203 6691 8798 2092 8263 3755 14 3600 570 4527 200 9718 6771 1995 8902 5446 768 1103 6520
(7.11)
c2(t) =
15 6304 7621 16 6498 9209 17 7293 6786 18 5950 1708 19 8521 1793 20 6174 7854 21 9773 1190 22 9517 10268 23 2181 9349 24 1949 5560 25 1556 555 26 8600 3827 27 5072 1057 28 7928 3542 29 3226 3762 0 7045 2420 1 9645 2641 2 2774 2452 3 5331 2031 4 9400 7503 5 1850 2338 6 10456 9774 7 1692 9276 8 10037 4038 9 3964 338 10 2640 5087 11 858 3473 12 5582 5683 13 9523 916
... ... ...
14 4107 1559 15 4506 3491 16 8191 4182 17 10192 6157 18 5668 3305 19 3449 1540 20 4766 2697 21 4069 6675 22 1117 1016 23 5619 3085 24 8483 8400 25 8255 394 26 6338 5042 27 6174 5119 28 7203 1989 29 1781 5174 0 1464 3559 1 3376 4214 2 7238 67 3 10595 8831 4 1221 6513 5 5300 4652 6 1429 9749 7 7878 5131 8 4435 10284 9 6331 5507 10 6662 4941 11 9614 10238 12 8400 8025 13 9156 5630 14 7067 8878
... ... ...
15 9027 3415 16 1690 3866 17 2854 8469 18 6206 630 19 363 5453 20 4125 7008 21 1612 6702 22 9069 9226 23 5767 4060 24 3743 9237 25 7018 5572 26 8892 4536 27 853 6064 28 8069 5893 29 2051 2885 0 10691 3153 1 3602 4055 2 328 1717 3 2219 9299 4 31939 7898 5 617 206 6 8544 1374 7 10676 3240 8 6672 9489 9 3170 7457 10 7868 5731 11 6121 10732 12 4843 9132 13 580 91 14 6267 9290 15 3009 2268 16 195 2419 17 8016 1557 18 1516 9195 19 8062 9064 20 2095 8968 21 753 7326 22 6291 3833 23 2614 7844 24 2303 646
... ... ...
25 2075 611 26 4687 362 27 8684 9940 28 4830 2065 29 7038 1363 0 1769 7837 1 3801 1689 2 10070 2359 3 3667 9918 4 1914 6920 5 4244 5669 6 10245 7821 7 7648 3944 8 3310 5488 9 6346 9666 10 7088 6122 11 1291 7827 12 10592 8945 13 3609 7120 14 9168 9112 15 6203 8052 16 3330 2895 17 4264 10563 18 10556 6496 19 8807 7645 20 1999 4530 21 9202 6818 22 3403 1734 23 2106 9023 24 6881 3883 25 3895 2171 26 4062 6424 27 3755 9536
Addresses of parity bit accumulators for rate R = 8/9, nld pc= 64800 bits
c1(t) =
0 6235 2848 3222 1 5800 3492 5348 2 2757 927 90 3 6961 4516 4739 4 1172 3237 6264 5 1927 2425 3683 6 3714 6309 2495 7 3070 6342 7154 8 2428 613 3761 9 2906 264 5927 10 1716 1950 4273 11 4613 6179 3491 12 4865 3286 6005 13 1343 5923 3529 14 4589 4035 2132 15 1579 3920 6737 16 1644 1191 5998 17 1482 2381 4620 18 6791 6014 6596 19 2738 5918 3786
(7.13)
c2(t) =
0 5156 6166 1 1504 4356 2 130 1904 3 6027 3187 4 6718 759 5 6240 2870 6 2343 1311 7 1039 5465 8 6617 2513 9 1588 5222 10 6561 535 11 4765 2054 12 5966 6892 13 1969 3869 14 3571 2420 15 4632 981 16 3215 4163 17 973 3117 18 3802 6198 19 3794 3948 0 3196 6126 1 573 1909 2 850 4034 3 5622 1601 4 6005 524 5 5251 5783 6 172 2032 7 1875 2475 8 497 1291 9 2566 3430 10 1249 740 11 2944 1948 12 6528 2899
... ... ...
13 2243 3616 14 867 3733 15 1374 4702 16 4698 2285 17 4760 3917 18 1859 4058 19 6141 3527 0 2148 5066 1 1306 145 2 2319 871 3 3463 1061 4 5554 6647 5 5837 339 6 5821 4932 7 6356 4756 8 3930 418 9 211 3094 10 1007 4928
... ... ...
11 3584 1235 12 6982 2869 13 1612 1013 14 953 4964 15 4555 4410 16 4925 4842 17 5778 600 18 6509 2417 19 1260 4903 0 3369 3031 1 3557 3224 2 3028 583 3 3258 440 4 6226 6655 5 4895 1094 6 1481 6847 7 4433 1932 8 2107 1649 9 2119 2065 10 4003 6388 11 6720 3622 12 3694 4521 13 1164 7050 14 1965 3613 15 4331 66 16 2970 1796 17 4652 3218 18 1762 4777 19 5736 1399 0 970 2572 1 2062 6599 2 4597 4870 3 1228 6913 4 4159 1037
... ... ...
5 2916 2362 6 395 1226 7 6911 4548 8 4618 2241 9 4120 4280 10 5825 474 11 2154 5558 12 3793 5471 13 5707 1595 14 1403 325 15 6601 5183 16 6369 4569 17 4846 896 18 7092 6184 19 6764 7127 0 6358 1951 1 3117 6960 2 2710 7062 3 1133 3604 4 3694 657 5 1355 110 6 3329 6736 7 2505 3407 8 2462 4806 9 4216 214 10 5348 5619 11 6627 6243 12 2644 5073 13 4212 5088 14 3463 3889 15 5306 478 16 4320 6121
... ... ...
17 3961 1125 18 5699 1195 19 6511 792
0 3934 2778 1 3238 6587 2 1111 6596 3 1547 6226 4 1446 3885 5 3907 4043 6 6839 2873 7 1733 5615 8 5202 4269 9 3024 4722 10 5445 6372 11 370 1828 12 4695 1600 13 680 2074 14 1801 6690 15 2669 1377 16 2463 1681 17 5972 5171 18 5728 4284 19 1696 1459
Addresses of parity bit accumulators for rate R = 9/10, nld pc= 64800 bits
c1(t) =
0 5611 2563 2900 1 5220 3143 4813 2 2481 834 81 3 6265 4064 4265 4 1055 2914 5638 5 1734 2182 3315 6 3342 5678 2246 7 2185 552 3385 8 2615 236 5334 9 1546 1755 3846 10 4154 5561 3142 11 4382 2957 5400 12 1209 5329 3179 13 1421 3528 6063 14 1480 1072 5398 15 3843 1777 4369 16 1334 2145 4163 17 2368 5055 260
(7.15)
c2(t) =
0 6118 5405 1 2994 4370 2 3405 1669 3 4640 5550 4 1354 3921 5 117 1713 6 5425 2866 7 6047 683 8 5616 2582 9 2108 1179 10 933 4921 11 5953 2261 12 1430 4699 13 5905 480 14 4289 1846 15 5374 6208 16 1775 3476 17 3216 2178 0 4165 884 1 2896 3744 2 874 2801 3 3423 5579 4 3404 3552 5 2876 5515 6 516 1719 7 765 3631 8 5059 1441 9 5629 598 10 5405 473 11 4724 5210 12 155 1832
... ... ...
13 1689 2229 14 449 1164 15 2308 3088 16 1122 6669 17 2268 5758 0 5878 2609 1 782 3359 2 1231 4231 3 4225 2052 4 4286 3517 5 5531 3184 6 1935 4560 7 1174 131 8 3115 956 9 3129 1088 10 5238 4440
... ... ...
11 5722 4280 12 3540 375 13 191 2782 14 906 4432 15 3225 1111 16 6296 2583 17 1457 903
0 855 4475 1 4097 3970 2 4433 4361 3 5198 541 4 1146 4426 5 3202 2902 6 2724 525 7 1083 4124 8 2326 6003 9 5605 5990 10 4376 1579 11 4407 984 12 1332 6163 13 5359 3975 14 1907 1854 15 3601 5748 16 6056 3266 17 3322 4085 0 1768 3244 1 2149 144 2 1589 4291 3 5154 1252 4 1855 5939
... ... ...
5 4820 2706 6 1475 3360 7 4266 693 8 4156 2018 9 2103 752 10 3710 3853 11 5123 931 12 6146 3323 13 1939 5002 14 5140 1437 15 1263 293 16 5949 4665 17 4548 6380 0 3171 4690 1 5204 2114 2 6384 5565 3 5722 1757 4 2805 6264 5 1202 2616 6 1018 3244 7 4018 5289 8 2257 3067 9 2483 3073 10 1196 5329 11 649 3918 12 3791 4581 13 5028 3803 14 3119 3506 15 4779 431 16 3888 5510
... ... ...
17 4387 4084 0 5836 1692 1 5126 1078 2 5721 6165 3 3540 2499 4 2225 6348 5 1044 1484 6 6323 4042 7 1313 5603 8 1303 3496 9 3516 3639 10 5161 2293 11 4682 3845 12 3045 643 13 2818 2616 14 3267 649 15 6236 593 16 646 2948 17 4213 1442 0 5779 1596 1 2403 1237 2 2217 1514 3 5609 716 4 5155 3858 5 1517 1312 6 2554 3158 7 5280 2643 8 4990 1353 9 5648 1170 10 1152 4366 11 3561 5368 12 3581 1411 13 5647 4661 14 1542 5401 15 5078 2687 16 316 1755 17 3392 1991